Electronic circuits and other circuits, devices or systems often contain large linear subnetworks of passive components. Such subnetworks may represent, by way of example, interconnect information automatically extracted from large RLC network layouts, models of integrated circuit packages, or models of wireless propagation channels. Often these subnetworks are so large that they need to be replaced by much smaller reduced-order models, before any numerical simulation becomes feasible. The process of generating such reduced-order models is referred to herein as reduced-order macromodeling, or more generally, reduced-order modeling. Ideally, the resulting reduced-order models will produce a good approximation of the input-output behavior of the original subnetwork, at least in a limited domain of interest, such as a particular frequency range.
In recent years, reduced-order modeling techniques based on Padé approximation have been recognized to be powerful tools for various circuit simulation tasks. The first such technique was asymptotic waveform evaluation, which uses explicit moment matching. More recently, the attention has moved to reduced-order models generated by means of Krylov-subspace algorithms, which avoid the typical numerical instabilities of explicit moment matching.
An approach known as PVL, and its multi-port version MPVL, use variants of the Lanczos process to stably compute reduced-order models that represent Padé or matrix-Padé approximations of the circuit transfer function.
The SyPVL approach, and its multi-port version SyMPVL, are versions of PVL and MPVL, respectively, that are tailored to RLC circuits. By exploiting the symmetry of RLC transfer functions, the computational costs of SyPVL and SyMPVL are only half of those of general PVL and MPVL. The Arnoldi process is another popular Krylov-subspace algorithm. Arnoldi-based reduced-order model techniques have recently been proposed. These models are not defined by Padé approximation, and as a result, in general, they are not as accurate as a Padé-based model of the same size. In fact, Arnoldi-based models are known to match only half as many moments as Lanczos-based models. An example of an Arnoldi-based reduced-order modeling technique is the PRIMA technique, described in A. Odabasioglu et al., “PRIMA: passive reduced-order interconnect macromodeling algorithm,” Tech. Dig. 1997 IEEE/ACM International Conference on Computer-Aided Design, pp. 58–65, Los Alamitos, Calif., 1997, which is incorporated by reference herein.
In many applications, in particular those related to VLSI interconnect, the reduced-order model is used as a substitute for the full-blown original model in higher-level simulations. In such applications, it is very important for the reduced-order model to maintain the passivity properties of the original circuit. It has been shown that the SyMPVL technique is passive for RC, RL, and LC circuits. However, the Padé-based reduced-order model that characterizes SyMPVL cannot be guaranteed to be passive for general RLC circuits. On the other hand, the Arnoldi-based reduction technique PRIMA produces passive reduced-order models for general RLC circuits. PRIMA employs a block version of the Arnoldi process and then obtains reduced-order models by projecting the matrices defining the RLC transfer function onto the Arnoldi basis vectors.
While PRIMA generates provably passive reduced-order models, it does not preserve other structures, such as reciprocity or the block structure of the circuit matrices, inherent to RLC circuits. This has motivated the development of algorithms such as ENOR and its variants that generate passive and reciprocal reduced-order models, yet still match as many moments as PRIMA. However, the moment-matching property of the PRIMA models is not optimal. In fact, the PRIMA models match only half as many moments as optimal, but non-passive, moment-matching techniques such as SyMPVL.
Accordingly, a need exists for an improved reduced-order modeling technique that overcomes the disadvantages of PRIMA.